Present Value Comparison
Construction Engineering 221
Economic Analysis
Present Value Comparison
• Present Worth is used to establish a means
for comparing projects with different cash
flows over different periods.
• Discount all future receipts and
disbursement to current dollars and choose
project with highest worth, or Present Value
Present Value Comparison
• Can assume interest rate and compare
present value or can assume cash flows and
compare interest rates (rate of return
method)
• ROI (return on investment) as used in the
book is the same as interest rate
• Present worth is the excess present value of
one project over another
Present Value Comparison
• Present value of $100 today is $100
• Present value of $105 you will receive one
year from now is $100 (assuming a 5%
interest rate
• Therefore, the present worth of any
investment that does not pay you more than
105 dollars one year from today is zero or
less
Present Value Comparison
• Negative present worth projects use a
minimization of loss criteria
• Positive present worth projects use a
maximization of return on capital criteria
• Interest rate used in present worth can be
taken from a variety of sources. Most
common (conservative) is to use the riskfree rate
Present Value Comparison
• Calculate the risk free rate from government
bond and note auctions (cnnfn.com)
Present Value Comparison
• Some companies have a hurdle rate or an
average annual return rate that they use in
their calculations
• Can vary the interest rate used based on risk
associated with the project (higher risk =
higher interest rate)
Present Value Comparison
• Compound interest is interest earned on
principal AND interest earned to date
• If interest is paid only on the original
investment, then it is simple interest
• Simple interest is uncommon in engineering
problems, but can apply to certain payouts
where interest is paid (literally) each year
and the investment is re-started
Present Value Comparison
• The book uses a trial and error approach to
solving ROR problems, but can also
interpolate from the tables
• Also, many pocket calculators and on-line
rate calculators can generate ROR
comparisons
Present Value Comparison
• Example- which of the following options is
best:
– Option 1 requires $1000 initial investment and
pays $120 per year for 10 years
– Option 2 requires $2500 initial investment and
pays $250 per year for 12 years
– General form is P = A (P/A, i, n)
Present Value Comparison
• Option 1: 1000 = 120 (P/A, i, 10)
– (P/A, i, 10) = 8.33, look at n = 10 lines in
tables, find i where P/A is closest to 8.33, or i =
3.5% (page 106)
– Option 2, same logic, (P/A. i, 12) = 10
(2500/250); look at n = 12 lines for P/A closest
to 10, or i = 3% (page 104)
Present Value Comparison
• Therefore, Option 1 is the best choice, or
provides the maximum rate or return FROM
AMONG THE AVAILABLE CHOICES
• Tomorrow in class- sample problems on
ROR and present worth